# Linear Equations In Two Variables – Class 9/ Maths.

Chapter 4 of NCERT/CBSE class 9 Maths is about Linear equations in two variables. Here in this lesson you can find practice problems for this chapter.

CBSE CLASS 9 MATHEMATICS
Linear Equations In Two Variables – Chapter 4 / Sample Papers.

1. If the point (3, 4) lies on the line 2y = ax + 8, then find the value of a?
Solution:
Since the point (3, 4) lies on the line 2y = ax +8, we can write 2 x 4 = a x 3 + 8.
8 = 3a + 8
3a = 8 – 8 = 0
Therefore, a = 0
2. Find two solutions for the equation 3x – 2y = 6.
Solution:
Taking x = 0, we get -2y = 6
That is, y = 6/ (-2) = -3.
So (0, -3) is a solution of the given equation.
Similarly, by taking y = 0, we get 3x = 6
That is x = 6/3 = 2.
So (2, 0) is a solution of the given equation.
3. Show that the points (0, 7), (1, 5), (2, 3) and (4, -1) lie on the graph of the linear equation 2x + y = 7.
Solution:
Given equation is 2x + y = 7
At (0, 7); LHS = 2 x 0 + 7 = 0 + 7 = 7 = RHS.
At (1, 5); LHS = 2 x 1 + 5 = 2 + 5 = 7 = RHS.
At (2, 3); LHS = 2 x 2 + 3 = 4 + 3 = 7 = RHS.
At (4, -1); LHS = 2 x 4 + (-1) = 8 + (-1) = 7 = RHS.
4. Find the value of k, if x = 3, y = 4 is a solution of the equation 3x – y = k.
Solution:
Given 3x – y = k
Put x = 3 and y = 4 in the given equation 3x – y = k
3 x 3 – 4 = k
9 – 4 = k
5 = k.
So the value of k is 5.
5. Determine the point on the graph of the linear equation 2x + 3y = 8, whose ordinate is 2 times its abscissa.
Solution:
Given ordinate is 2 times its abscissa, which means that y = 2x.
Put y = 2x in the given equation 2x + 3y = 8, we get 2x + 3(2x) = 8.
2x + 6x = 8
8x = 8
x = 8/8 = 1.
6. Solve the equation 2x + 1 = x – 3.
Solution:
2x + 1 = x -3
2x – x = -3 -1
x = -4
7. Find the co-ordinates of points where the graph of the equation x + 2y = 8 intersects x axis and y axis.
Solution:
Given equation is x + 2y = 8.
For intersection with x axis, y = 0.
Therefore, x = 8.
So the coordinates are (8, 0).
For intersection with y axis, x = 0.
2y = 8
y = 8/2 = 4
So the coordinates are (0, 4).